Materials exploration method and materials exploration support system

Abstract

To reduce the number of searches required for finding a material having a characteristic sufficiently matching an intended characteristic in an art searching for the material having the intended characteristic based on information on a structure of the material and the like.SOLUTION: A method of searching for a material having an intended characteristic is configured to repeat: a process of adjusting a characteristic-amount vector, having a correlation with an object characteristic value, of each of a plurality of candidate materials, and using an object characteristic value and characteristic-amount vector of a known material having the object characteristic value known to obtain a probability distribution of the object characteristic value from the characteristic-amount vector about each of the candidate materials according to an algorithm of a Gaussian process regression; a process of selecting a material of which the object characteristic value is predicted to be closest to a target value, of the material candidate according to the algorithm of Thompson Sampling on the basis of the probability distribution of the object characteristic value of each candidate material; and a process of obtaining an object characteristic value of the selected material until a prescribed condition is established, including the selected material having the object characteristic value obtained in the known material having the object characteristic value known.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to a method for searching for materials having desired properties based on information such as the structure of the material using machine learning technology, and a system for supporting the search for materials. More specifically, the present invention relates to a method and system for expressing characteristics such as the structure of a candidate material (candidate material) with a plurality of parameters (called "descriptors"), setting a search space with these descriptors as variables, and searching for materials having the desired properties or properties close to those properties in the search space, as in the Bayesian optimization method. [Background technology]

[0002] In the field of materials science, various techniques have been proposed to predict the properties of individual materials based on information on the structures of various materials, such as the properties of atoms and molecular groups that constitute the materials, the bond relationships between atoms and molecules, the crystal structure, and the arrangement of atoms in the structure, and to search for materials suitable for any purpose (such as materials with properties advantageous for rechargeable batteries and solar power generation) from among those materials using machine learning techniques. For example, Non-Patent Document 1 proposes a method of efficiently searching for materials with low ion migration energy suitable as battery materials using a Bayesian optimization algorithm. In the material search method described in this document, in brief, first, for materials consisting of five constituent elements, multiple descriptors that represent the characteristics of the structure of the material that are predicted to determine the ion migration energy are selected, and a space in which the multiple descriptors are variables and points (material points) specified by the descriptors of various materials that can be candidates are arranged is set as a search space. Then, in the search space, the ion migration energy Eb is precisely calculated for five arbitrarily selected material points using DFT (density functional theory). In this example, since it is desired to search for a material with the smallest Eb, -Eb is used as the characteristic value for each material point, and the material point with the largest characteristic value is searched for. Then, according to a Gaussian process regression model using the pairs of the descriptors and characteristic values ​​of the above five material points as training data, the average value and variance of the characteristic values ​​of each material point in the search space are predicted, and the material point with the largest acquisition function given by these predicted values ​​is selected, and the characteristic value of the selected material point is calculated using DFT. Here, the material point with the largest acquisition function is a point whose characteristic value is expected to approach the maximum value (Eb becomes smaller), so the selected material point and its characteristic value are included in the training data, and the above process is repeated, and further a material point that gives a characteristic value close to the maximum value is determined. Thus, by repeating this process, a material with the smallest Eb is found among the material points arranged in the search space.Non-Patent Document 1 reports that in the above-mentioned Bayesian optimization material search method, the search speed can be improved by grouping a plurality of descriptors according to their properties and expressing the objective function that gives the characteristic value as the sum of the objective functions of the groups of each descriptor (aBO: additive Bayesian Optimization).

[0003] As a technique for predicting the physical properties of a material from its crystal information using deep learning technology, Non-Patent Document 2 proposes a technique called CGCNN (Crystal Graph Convolutional Neural Networks). In addition, regarding a Bayesian optimization algorithm, Non-Patent Document 3 proposes an algorithm called ALEBO (adaptive linear embedding Bayesian Optimization) as a technique for achieving more efficient search when the dimension of the descriptor in the search space is high. Non-Patent Document 4 proposes a technique called CIQ (Contour Integral Quadrature) as an algorithm for quickly calculating the inverse matrix of the kernel in processing a Gaussian process regression model. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] "Bayesian-Driven First-Principles Calculations for Accelerating Exploration of Fast Ion Conductors for Rechargeable Battery Application" R. Jalem, et al., Scientific REPorTS,(2018) 8:5845, DOI:10.1038 / s41598-018-23852-y [Non-Patent Document 2] "Crystal Graph Convolutional Neural Networks for an Accurate and Interpretable Prediction of Material Properties" T. Xie and JCGrossman, Physical Review Letters, 120(45301), 2018. URL https: / / journals.aps.org / prl / abstract / 10.1103 / PhysRevLett.120.145301 [Non-Patent Document 3] "Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization", B.Letham, et al., In NeurIPS, 2020. URL https: / / arxiv.org / abs / 2001.11659 [Non-Patent Document 4] "Fast Matrix Square Roots with Applications to Gaussian Processes and Bayesian Optimization", G.Pleiss, et al., In NeurIPS, 2020. URL https: / / arxiv.org / abs / 2006.11267 Summary of the Invention [Problem to be solved by the invention]

[0005] In the technology for searching for a material having a target characteristic based on information such as the structure of the material using the machine learning technology as described above, a material having a value as close as possible to a target value for a certain characteristic is searched for, in other words, a material that optimizes a certain characteristic is searched for. In a specific procedure of this technology, to put it simply, first, among a plurality of materials (candidate materials) that are candidates for a material having a target characteristic, for materials whose values ​​of the characteristic to be optimized (hereinafter referred to as "target characteristic values") are known, information on their structures, etc. is used as input values ​​for learning, and the known target characteristic values ​​of these materials are used as output values ​​for learning, and a regression process of the target characteristic values ​​of the candidate materials whose target characteristics are unknown, that is, calculation of the predicted value or its probability distribution of the target characteristic values ​​using information such as the structure of each material, is performed. Then, based on the regression results of the target characteristic values ​​of each material, a material whose target characteristic value is estimated to be closest to the target value is selected, and the target characteristic value of the selected material is determined with high accuracy, for example, by actual measurement or precision calculation. If the target property value of the selected material sufficiently matches the desired property, the search is completed, whereas if further optimization of the target property is to be attempted, the information on the currently selected material's structure, etc. and the target property value are added to the learning input and output values, and the above procedure is repeated. When the search procedure is repeated, the number of materials whose target property values ​​are known with high accuracy increases successively, and at the same time, the regression accuracy of the output value is improved, so that the property values ​​of each candidate material can be predicted with higher accuracy, and a material having a property value closer to the target value can be found.

[0006] In the above-mentioned material search technology, in order to achieve material search at lower cost or with less labor, it is preferable that the target property value is optimized as quickly as possible, that is, the number of searches required to find a material having properties that sufficiently match the target property can be reduced. In this regard, according to research by the inventor of the present invention, it has been found that the number of searches required to find a material having properties that sufficiently match the target property can be significantly reduced by appropriately selecting or adjusting the process of selecting a material based on the regression result of the target property value (output value) of the candidate material, the method of preparing information such as the structure of the candidate material or the descriptor (input value) used in the regression process, or the algorithm used in the regression process. This knowledge is utilized in the present invention.

[0007] Thus, one objective of the present invention is to reduce the number of searches required to find a material having properties that match the desired properties as closely as possible or sufficiently in a technique that uses machine learning technology to search for a material having desired properties based on information such as the structure of the material.

[0008] Another object of the present invention is to provide a method and system for the above-mentioned material search technology, which is capable of reducing the number of times a material is searched for by improving the process of selecting a material based on the regression results of the output values ​​of the candidate materials, the manner of preparing the input values ​​of the candidate materials used in the regression process, or the algorithm used in the regression process. [Means for solving the problem]

[0009] According to the present invention, the above object is achieved in one aspect by a method for searching for a material having a desired property, the method comprising: A first step of preparing a feature vector having a correlation with a target characteristic value for each of a plurality of candidate materials; a second step of calculating a probability distribution of the target characteristic value from the feature vector for each of the candidate materials in accordance with an algorithm of a Gaussian process regression model using a target characteristic value of a known material among the candidate materials, the target characteristic value of which is known, and the feature vector; a third step of selecting, from among the candidate materials, a material whose target property value is predicted to be closest to its target value according to a Thompson selection algorithm based on a probability distribution of the target property value of each of the candidate materials; a fourth step of determining the target property value of the selected material; Including, The selected material, whose target characteristic value has been determined in the fourth step, is included in known materials whose target characteristic value is known, and the second, third and fourth steps are repeated until a predetermined condition is met. This is achieved by:

[0010] In the above configuration, A "material" can be any inorganic or organic material. The "characteristic" may be any physical or chemical characteristic, such as the size of the band gap or the magnitude of the ionization energy, and the "target characteristic value" is an index value representing the above characteristic. A "material having a target characteristic" is a material having advantageous characteristics for various applications, such as rechargeable batteries and photovoltaic power generation, and specifically, a material whose target characteristic value matches or is sufficiently close to a target value that is appropriately set. The allowable difference between the target characteristic value and the target value may be set appropriately. A "candidate material" is a material that is a candidate for a material having the desired properties, that is, a material that is the subject of search. The "feature vector" is a value that represents the characteristics of the structure of a material, and is a vector of a predetermined dimension that is composed of a plurality of values, i.e., descriptors, that are correlated with the target characteristic value. The dimension of this vector may be set arbitrarily and appropriately. In the "Gaussian process regression model algorithm", a probability distribution of predicted values ​​of target property values ​​for each candidate material is determined based on a kernel given using components of feature vectors of materials (known materials) among the candidate materials whose target property values ​​are known, and the known target property values. As a specific algorithm, any Gaussian process regression model algorithm may be used. Note that the predicted value of the target property value is the target property value predicted by regression processing or the value of a function thereof. In the "Thompson Sampling Algorithm", an expected value for the target characteristic value is calculated from the probability distribution of the predicted values ​​for the target characteristic value for each of the candidate materials. The probability that each candidate material should be selected is calculated from these expected values ​​using a softmax function, and the material whose target characteristic value is predicted to be closest to the target value is randomly selected from among the candidate materials according to this probability. In the "fourth step of determining the target property value of the selected material", the target property value of the selected material may be determined by actual measurement or by any precise calculation. The "predetermined condition" for terminating the repetitive execution of the "second, third and fourth steps" may be set arbitrarily, and may be, for example, that the target property value determined in the fourth step of the material selected in the third step sufficiently matches the target value, or that the number of searches (the number of times the second, third and fourth steps are repeated) has reached a predetermined number, which may be set arbitrarily.

[0011] According to the above configuration, first, a feature vector of a predetermined dimension of a plurality of candidate materials is prepared. In other words, this corresponds to preparing a "search space" in which points (material points) representing each candidate material are distributed in a space of the dimension of the feature vector. Each material point in the search space has a true target characteristic value, but most of them are unknown. Therefore, in the search for a material to be targeted by the present invention, one of each candidate material is selected one by one, and while checking its true target characteristic value, an attempt is made to find a material point having a target characteristic value as close as possible to the target value. In the search for such a material, the object of the method of the present invention is to reduce the number of times (number of searches) of selecting one of each candidate material and checking the true target characteristic value as much as possible.

[0012] Therefore, in the method of the present invention described above, in order to minimize the number of searches, predictions of the target property value at each material point in the search space are made according to a Gaussian process regression model algorithm using the target property values ​​and feature vectors of known materials, some of which are candidate materials and have known target property values. In this case, as described above, a probability distribution for the target property value at each material point is determined, and based on this probability distribution, according to the above Thompson extraction algorithm, a material whose true target property value should be confirmed next among the material points whose true target property value is unknown is selected, i.e., the material whose target property value is predicted to be closest to the target value.

[0013] According to the configuration of the method of the present invention, unlike the material search method in Non-Patent Document 1 (a Bayesian optimization method that selects the maximum value among the values ​​of the acquisition function, which is a continuous function), the search is performed by a method in which the next search point is selected based on the prediction of the individual target property values ​​at each material point that is discretely distributed in the search space, that is, a "bandit optimization" method. According to the research of the inventor of the present invention, it is possible to bring the newly searched target property value closer to the target value faster than in the case of the above-mentioned Bayesian optimization using the acquisition function, and it is possible to discover a "material having the desired property" with fewer searches.

[0014] In the embodiment of the configuration of the method of the present invention described above, in the first step, a feature vector may be calculated based on the crystal information of each of the multiple candidate materials. Here, the crystal information of the candidate material may be information in any format that describes the crystal structure of the material, for example, information in the format of CIF (Crystallograhic Information File), which is a "common data format for crystallographic information". In addition, the calculation of the feature vector based on the crystal information may be performed using a regression analyzer that calculates the target characteristic value from the crystal information of any material, for example, a regression analyzer configured to calculate the target characteristic value from the crystal information of the material by any machine learning algorithm. According to the research of the inventor of the present invention, it has been found that a regression analyzer configured according to the algorithm of the crystal graph convolution neural network (CGCNN) described in Non-Patent Document 2 can be suitably used as such a regression analyzer. Note that, when a regression analyzer using CGCNN is used, in the learning stage, the CIF format of the multiple materials and the target characteristic value obtained from the crystal information by first-principles calculation are used as learning data to learn to calculate the target characteristic value from the crystal information. Here, the first-principles calculation is a quantum chemical approximation calculation from crystal information, and an approximation value of the target characteristic value such as the size of the band gap is obtained. The approximation value of the target characteristic value here is usually less accurate than the target characteristic value obtained by actual measurement or precise calculation in the fourth step of the method of the present invention. A vector of a predetermined dimension used for calculating the target characteristic value in the regression analyzer using CGCNN may be adopted as the feature vector. According to the research of the inventor of the present invention, it has been found that the number of searches can be reduced by adopting multiple component values ​​(128-dimensional intermediate vector) immediately before calculating the target characteristic value in the regression analyzer using CGCNN for the feature vector.[The component values ​​of the above intermediate vectors in the CGCNN regression analyzer are values ​​that are directly used to calculate an approximation of the target characteristic value, and therefore are considered to have a stronger correlation with the target characteristic value than values ​​related to the structure, etc., described in the crystal information in CIF format. Therefore, since they have good performance as a descriptor for the target characteristic value, they are considered to have improved prediction accuracy for the target characteristic value in the regression process, and to have greatly contributed to reducing the number of searches.]

[0015] In addition, when using the above-mentioned regression analyzer using CGCNN, the intermediate vector obtained from the regression analyzer using CGCNN has 128 dimensions, which is relatively high, and therefore the computation load in the second and third steps may be large. Therefore, preferably, a principal component analysis is performed on the group of intermediate vectors of the candidate materials obtained from the regression analyzer using CGCNN, and a predetermined number of principal components (which may be set arbitrarily) obtained by the analysis may be adopted as the feature vector to be used in the second and third steps. The principal component analysis may be performed by an arbitrary algorithm. By such processing, a feature vector having a lower dimension than the intermediate vector is obtained, and the computation load in the second and third steps is reduced. In this regard, according to the research of the inventor of the present invention, it has been found that the number of searches can be suitably reduced by using the first principal component to the twelfth principal component as components of the feature vector. This is considered to be because, in such a configuration, the prediction accuracy of the target characteristic value in the regression processing can be well maintained.

[0016] Furthermore, in the second step of the method of the present invention, as described above, a regression process is performed to obtain a probability distribution for each target characteristic value of a candidate material from the target characteristic value and feature vector of a known material according to the algorithm of the Gaussian process regression model. When the dimension of the feature vector and the number of material points are large, the calculation load also becomes large. In this regard, if a Gaussian process regression model using a Mahalanobis kernel used in an algorithm called ALEBO described in Non-Patent Document 3 is adopted as the algorithm of the Gaussian process regression model used for the calculation, the range of the feature vector of the known material used for the kernel calculation is suitably reduced, and the calculation load is reduced. Therefore, in the method of the present invention, a Mahalanobis kernel may be used as a kernel that gives a probability distribution according to the ALEBO algorithm in the algorithm of the Gaussian process regression model. In addition, in order to further reduce the calculation load in the calculation of the probability distribution using such a Mahalanobis kernel, the CIQ algorithm described in Non-Patent Document 4 may be used for the calculation of the inverse matrix of the Mahalanobis kernel, but is not limited thereto.

[0017] Furthermore, in the second and third steps of the above-mentioned method of the present invention, a probability distribution for the target property value is obtained by a Gaussian process regression model algorithm, and a material whose target property value is predicted to be closest to the target value is selected by a Thompson sampling algorithm based on the probability distribution. However, according to research by the inventors of the present invention, it has been found that the number of searches can be reduced by obtaining a probability distribution for the target property value, not for the target property value itself, but for the inverse of the Poisson loss or normalized Poisson loss between the target property value and its target value, and selecting a material point from among the candidate materials by Thompson sampling according to a probability calculated so that the larger the expected value of the Poisson loss or the inverse of the normalized Poisson loss, the larger the probability becomes. In the present invention, the Poisson loss Lp is calculated by multiplying the known or predicted value y i , the target value of the target characteristic y tUsing the following-defined quantity (which may be different from the definition of normal Poisson loss). Lp = y i -y t ·log y i …(1) Furthermore, the normalized Poisson loss is a value obtained by normalizing the Poisson loss of Equation (1) with a target value, and is given by the following equation. Lp’ = y i / y t -log(y i / y t ) …(1a) In the above, Equation (1) is used when y t <e (Napier's number), and Equation (1a) is used when y t is any positive number. Note that when y i ≦0, instead of the Poisson loss of Equation (1) or (1a), the square of the difference between the target characteristic value and its target value (square error)) Le = (y i -y t ) 2 …(1b) is used. Therefore, in the present invention, in the second process, the probability distribution of the target characteristic value is the probability distribution of the reciprocal of the Poisson loss, the normalized Poisson loss, or the square error between the target characteristic value and the target value, and in the Thompson sampling algorithm in the third process, among the candidate materials, the material for which the target characteristic value is predicted to be closest to the target value according to the probability calculated so that the expected value of the reciprocal of the Poisson loss, the normalized Poisson loss, or the square error is larger may be selected.

[0018] The method of the present invention described above is achieved by repeatedly performing a search for materials using a system that executes the first, second, and third processes. Therefore, according to another aspect of the present invention, a system for executing the first, second, and third processes in the method of the present invention described above is provided. According to the present invention, a system for assisting in the search for a material having a target characteristic, A first means for preparing a feature vector having a correlation with a target characteristic value for each of a plurality of candidate materials; a second means for calculating a probability distribution of the target characteristic value from the feature vector for each of the candidate materials in accordance with an algorithm of a Gaussian process regression model using a target characteristic value of a known material, the target characteristic value of which is known, and the feature vector; a third means for selecting, from among the candidate materials, a material whose target property value is predicted to be closest to its target value according to a Thompson selection algorithm based on a probability distribution for the target property value of each of the candidate materials; A system that includes The definitions of terms and preferred embodiments of the above system are the same as those of the method of the present invention. The above system of the present invention is realized by a computer device operating in accordance with a program. Effect of the Invention

[0019] As described above, in the method of the present invention, a search space in which material points specified by the feature vectors of each candidate material are distributed is first prepared, and in the search space, instead of Bayesian optimization in which the search points are considered as continuous functions, bandit optimization is used in which the search points are considered to exist discretely and the discrete search points are efficiently searched for by performing Thompson extraction. As a result, as will be described in the following embodiment section, it has been found that the speed at which the target property value of the selected material approaches the target value is increased, and materials can be searched for more quickly. Therefore, according to the present invention, the number of times that the true target property value of the material is detected until a material matching the target property is found is reduced, and it is expected that the cost, effort, labor, time, etc. required for material search can be significantly reduced. Such a method and system of the present invention can be used to search for materials having the target properties for various applications, and is expected to contribute to the discovery of new materials having more suitable properties.

[0020] Other objects and advantages of the present invention will become apparent from the following description of preferred embodiments of the invention. [Brief description of the drawings]

[0021] [Figure 1] FIG. 1 is a schematic diagram showing a computer used for implementing the method for searching for a material having target properties according to this embodiment. [Diagram 2] FIG. 2 is a block diagram showing the internal configuration of the system for supporting material exploration according to this embodiment. [Diagram 3] FIG. 3 is a diagram showing, in the form of a flow chart, the process steps in the method for searching for a material having target properties according to this embodiment. [Figure 4] Fig. 4(A) is a diagram for explaining the configuration of a regression analyzer used to generate a search space of candidate materials in the method according to the present embodiment. Fig. 4(B) is a schematic diagram for explaining the configuration of the search space of candidate materials in the method according to the present embodiment. [Diagram 5] Fig. 5(A) is a schematic diagram for explaining the probability distribution of the inverse of Poisson loss of the predicted property value of each candidate material calculated by the Gaussian process regression processing in the method according to the present embodiment. Fig. 5(B) is a schematic diagram for explaining the probability that each candidate material is selected as the material for which detection of the target property value is next performed, calculated in the Thompson extraction processing in the method according to the present embodiment. [Figure 6] FIG. 6 is a graph showing the change in the absolute value of error (MAE) between the characteristic value of the optimal material and the target value versus the number of searches (trials) when searching for materials in an experimental example using the method of this embodiment, the Bayesian optimization method, and the random extraction method. The characteristic value of the optimal material is the value closest to the target value among the characteristic values ​​obtained up to that point. In the experiment, trials (selection of candidate materials) were repeated 30 times in one search experiment, and the MAE was calculated for each trial, and the search experiment was performed for 50 cycles. In the figure, the value of the graph indicates the average value of the MAE in each trial in the 50-cycle search experiment. [Explanation of symbols]

[0022] 1. Computer main unit 2. Computer terminal 3. Monitor 4...Keyboard, mouse (input device) 10. Database BEST MODE FOR CARRYING OUT THEINVENTION

[0023] Computer device configuration The method for searching for materials having target properties according to this embodiment is executed using a computer device 1 of a type commonly used in this field, as illustrated in FIG. 1. Therefore, the system for supporting the search for materials having target properties according to this embodiment may be realized by the operation of a computer program in the computer device 1. The computer device 1 is equipped with a CPU, a storage device, and an input / output device (I / O) interconnected by a bidirectional common bus in a normal manner, and the storage device includes a memory that stores each program for executing the calculation process used in the calculation of this embodiment, and a work memory and a data memory that are used during the calculation. In addition, the operator's instructions to the computer device 1 and the display and output of the calculation results and other information are performed through a computer terminal device 2 connected to the computer device 1. The computer terminal device 2 is provided with a monitor 3 and an input device 4 such as a keyboard and a mouse in a normal manner, and when the program is started, the operator can use the input device 4 to give various instructions and inputs to the computer device 1 according to the display on the monitor 3 in accordance with the procedure of the program, and can visually confirm the calculation status and calculation results from the computer device 1 on the monitor 3. Furthermore, in this embodiment, as described later, information related to the structure of the materials to be searched, such as crystal information, is used, and the information on the materials may be acquired from any database, and therefore the computer device 1 may be able to access any database 10 by any method. It should be understood that the computer device 1 and the computer terminal device 2 may be equipped with other peripheral devices (such as a printer for outputting results, a storage device for inputting and outputting calculation conditions and calculation result information, etc.) that are not shown. When the computer device 1 is used to execute various processes or calculations described below, programs required for the various processes or calculations are started in a normal manner, and the implementer inputs data required for the calculation, calculation conditions at the time of calculation, and other various settings in the computer terminal device 2 according to the input procedure prepared in the program, and the calculation is started.Then, during or after the calculation is completed, the calculation result can be output via the computer terminal device 2 as appropriate.

[0024] In the method for searching for a material having a desired property according to this embodiment, the computer device 1 executes the process of generating a search space of candidate materials, Gaussian process regression in the search space, and selection of a material for which a target property value is to be detected next according to the Thompson extraction algorithm, among the processes described later with reference to Fig. 3, and the selection result is output to the computer terminal device 2 and displayed on a monitor or the like. Then, the implementer, referring to the result, executes detection of a target property value of the selected material with high accuracy by actual measurement or precise calculation experiment or simulation, and if the search is to be continued based on the detection result of the target property value, the detected target property value is input to the computer device 1, and the computer device 1 is used to repeat the Gaussian process regression in the search space and the material selection process according to the Thompson extraction algorithm.

[0025] In this embodiment, the candidate materials for the search may be any inorganic or organic material, and the properties to be searched may be any physical or chemical properties of the material, such as the size of the band gap, ionization energy, etc. Information on the structure of the material used to generate the search space may be any information that can be used to prepare a feature vector to be described later, such as, but not limited to, information described in a file in the CIF format, which is the "Common Data Format for Crystallographic Information."

[0026] Configuration of the materials exploration support system Referring to FIG. 2, the material search support system that executes processes from generating a search space of candidate materials to selecting a material for detecting target characteristic values ​​in the material search method according to this embodiment includes a search space generation unit, a regression processing unit, and a Thompson extraction unit.

[0027] In short, the search space generation unit executes a process of calculating a "feature vector" that is correlated with the target characteristic value for each candidate material based on information such as the structure of various materials that are candidates for a material having a target characteristic, i.e., a material whose physical or chemical characteristic value (target characteristic value) related to the use of the material is as close as possible to the target value. Here, the feature vector is a vector whose components (elements) are feature amounts (descriptors) that are set arbitrarily. Then, the search space generation unit further executes a process of accepting the known target characteristic value for a material among the candidate materials whose target characteristic value is known with high accuracy and associating the known target characteristic value with the feature vector of the corresponding material. In other words, in the search space generation unit, in a space of dimensions of the number of descriptors, points representing each candidate material (hereinafter referred to as "material points") are arranged and distributed at positions specified by the feature vector, and a state is formed in which some of them are associated with the known target characteristic value, and the space in that state is used as the search space. As described later, when the detection of the target property value of the selected candidate material is executed in the method of this embodiment, the newly detected target property value is associated with the feature vector of the corresponding material as a known target property value. In addition, if there is no known target property value in the initial stage of material search, a Thompson extraction unit described later may detect a target property value of a randomly selected material, and the detected target property value may be input as a known target property value.

[0028] The specific process of generating the search space may be achieved by any method, but the inventor of the present invention has found that a regression analyzer according to the CGCNN algorithm described in Non-Patent Document 2 is advantageously used, as will be described in detail later. When using such a regression analyzer, first, a regression analyzer is configured by machine learning processing so that any characteristic value of any material can be calculated from the crystal information of the CIF format of the material according to the CGCNN algorithm, and then, using the regression analyzer, the values ​​of multiple components obtained on the way to the calculation of the arbitrary characteristic value from the crystal information of the CIF format of each candidate material are extracted as "intermediate vectors". In the case of CGCNN, this intermediate vector is, for example, a 128-dimensional vector, and the dimension is too high to be used as a feature vector as it is in the subsequent calculations. Therefore, in this embodiment, in order to suitably reduce the dimension of such intermediate vectors, principal component analysis is preferably applied to the intermediate vectors for each candidate material, and the values ​​of the first principal component to any number of principal components (for example, the 12th principal component) are used as feature vectors. As will be understood from the experimental examples described later, it has been found that the use of the feature vectors of each candidate material obtained in the above manner allows the search for materials to be more suitably accomplished. Therefore, in one preferred embodiment, the search space generation unit may be configured to calculate intermediate vectors for each candidate material by a regression analyzer according to the CGCNN algorithm, and to adopt multiple principal components of each candidate material as feature vectors from principal component analysis of the intermediate vectors.

[0029] In the regression processing unit, in the above search space, the feature vector of the material whose target characteristic value is known and the target characteristic value are used, and a probability distribution of the predicted value of the target characteristic value at the material point of each candidate material is determined according to the algorithm of the Gaussian process regression model (the probability distribution of the predicted value of the target characteristic value is the distribution of the probability that the predicted value of the target characteristic value or its function value is each value. See FIG. 5(A) described later). In the algorithm of the Gaussian process regression model, any algorithm and kernel may be used, and according to the research of the inventor of the present invention, it has been found that the Gaussian process regression model in ALEBO using the Mahalanobis kernel described in Non-Patent Document 3 is advantageously used as the Gaussian process regression model. In addition, it has also been found that when calculating the probability distribution of the target characteristic value of each material point, the CIQ algorithm described in Non-Patent Document 4 is advantageously used for calculating the inverse matrix of the kernel matrix required in the calculation process. Therefore, in one preferred embodiment, in the regression processing unit, the Gaussian process regression model in ALEBO may be used as the Gaussian process regression model for regression processing, and the CIQ algorithm may be used to calculate the probability distribution of each material point.

[0030] In the Thompson extraction section, a material for which the target characteristic value is to be detected next is selected from among the candidate materials whose target characteristic value is unknown according to the Thompson extraction algorithm, using the probability distribution of the predicted value for the target characteristic value of each material point calculated by the regression processing section. Specifically, as will be described in detail later, the probability of each material point being selected is obtained from the probability distribution of the predicted value for the target characteristic value of each material point, and a material is selected according to the probability. Here, the probability of each material point being selected is determined to be larger as the expected value of the predicted value for the target characteristic value of each material point is larger. Therefore, in the case of this embodiment, the predicted value for the target characteristic value that determines the probability of each material point being selected, that is, the value to be optimized (also referred to as the "evaluation function"), is set to be larger as the target characteristic value approaches the target value. In this regard, according to the research of the inventor of the present invention, it has been found that the search for materials can be more suitably accomplished by using the inverse of the Poisson loss Lp (Equation (1)), normalized Poisson loss Lp' (Equation (1a)), or square error Le (Equation (1b)) between the target property value and the target value as the evaluation function. Therefore, in one preferred embodiment, the regression processing unit adopts the inverse of the Poisson loss Lp (or normalized Poisson loss Lp' or square error Le) between the target property value and the target value as the predicted value for the target property value of each material point, which is the value to be optimized, that is, as the evaluation function, and calculates the probability distribution of such evaluation function as the probability distribution for each candidate material, and the Thompson extraction unit may calculate the probability of each material point being selected from the probability distribution of the evaluation function so that the probability is higher as the expected value there is higher.

[0031] Thus, the information of the material selected by the Thompson extraction unit to be subjected to the next detection of the target property value is output, and the person conducting the search performs a precise detection of the target property value of the material. The detected target property value of the material is then input to the search space generation unit and associated with the corresponding material point.

[0032] Material exploration process (1) Overview In the material search targeted by this embodiment, generally speaking, a search space is prepared from information such as the structure of the candidate material, and then a regression process is performed to obtain a probability distribution of a predicted value of the target characteristic value of each candidate material using the feature vector and the target characteristic value of the known material, an extraction process is performed to extract one material whose target characteristic value is predicted to be close to its target value based on the probability distribution of each candidate material obtained by the regression process, and a detection process is performed to detect the target characteristic value of the material selected by the extraction process. A processing cycle consisting of the following is repeatedly executed until a predetermined condition that is arbitrarily set is satisfied, and an attempt is made to find a material having a target characteristic value sufficiently close to the target value. At that time, each time the detection process is executed, a new target characteristic value is detected and becomes known, and the material whose target characteristic value has been newly detected is added to the known materials in the regression process, and it is expected that each time the processing cycle is repeated, the accuracy of the regression process and the extraction process is improved, and the target characteristic value detected in the detection process approaches the target value (optimization). In this material search, particularly in this embodiment, the regression process is performed by a Gaussian process regression model, more preferably a Gaussian process regression model using the ALEBO algorithm, and the extraction process is performed according to the Thompson extraction algorithm, thereby reducing the number of searches. In addition, in generating the search space, a regression analyzer according to the CGCNN algorithm is preferably used, thereby improving the accuracy of the probability distribution of the predicted value for the target characteristic value of each candidate material in the regression process, thereby reducing the number of searches. Hereinafter, each process in the material search method according to this embodiment will be described with reference to Figures 3 to 5.

[0033] (2) Search space generation As described above, in the material search method of this embodiment, a search space is first prepared. As already described, the search space is a space in which a descriptor, which is an index value representing the characteristics of the structure of a material having a correlation with the target property value, is used as a variable, and in this space, the material points of each candidate material are distributed at positions specified by the feature vector. In this search space, the target property value of each candidate material is predicted based on the feature vector, so it is preferable that the index value used as the feature vector has a stronger correlation with the target property value. Therefore, in this embodiment, a regression analyzer is configured to regress the target property value from information such as the structure of the material according to an arbitrary machine learning technique, and the components used in the calculation of the target property value are extracted in the regression analyzer and used in the feature vector. According to this configuration, the components used in the calculation of the target property value in the regression analyzer have a stronger correlation with the target property value than the information such as the structure of the material itself, so that it is expected that the prediction of the target property value will be achieved better. In addition, since the regression analyzer used here is for obtaining a feature vector having a correlation with the target characteristic value, the target characteristic value calculated by the regression analyzer may be low-precision. Thus, the regression analyzer uses information such as the structure of the material as an input value, and performs learning by supervised learning using the target characteristic value as the correct label, and the target characteristic value used for the correct label may be an approximate value obtained at low cost or with low effort.

[0034] Referring to FIG. 3, in generating a search space using the regression analyzer, first, a target characteristic value, which may be low-precision, is calculated by an arbitrary method based on information on the structure of a material, such as crystal information, to be used as a correct label in the learning data of the regression analyzer (step 1). The target characteristic value at this stage is called a "pseudo characteristic value" to distinguish it from a highly accurate value described later. Such a "pseudo characteristic value" may be calculated by a first-principles calculation, such as a quantum chemical calculation. Next, the regression analyzer is trained by an arbitrary algorithm using information on the structure of a material, such as crystal information, as an input value and learning data using the pseudo characteristic value as a correct label (step 2). Then, when the regression analyzer is trained, information on the structure of a material, such as crystal information, of each candidate material is input to the regression analyzer (step 3), and a set of multiple component values ​​obtained during the calculation of the pseudo characteristic value is extracted as an "intermediate vector" and used for a feature vector (step 4).

[0035] The intermediate vector of the regression analyzer may be used as a feature vector as it is, but if the dimension of the intermediate vector is high, the subsequent calculation load may be large. Therefore, a principal component analysis may be applied to a group of vectors consisting of the intermediate vectors of each candidate material, and a vector formed by selecting an arbitrary number of principal components less than the dimension of the intermediate vector may be adopted as the feature vector (step 5).

[0036] As described above, when the feature vectors of each candidate material are calculated, the target characteristic values ​​of known materials whose target characteristic values ​​are known are input, and the known target characteristic values ​​are associated with the feature vectors of the corresponding materials (step 6).

[0037] Specifically, in one aspect of this embodiment, as a regression analyzer for obtaining the above feature vector, a regression analyzer configured by the CGCNN algorithm described in Non-Patent Document 2 is preferably used as mentioned above. In such a regression analyzer using CGCNN, as shown in FIG. 4(A), when information described in a crystal information file (CIF) is input, a target characteristic value is output through a calculation process according to the CGCNN algorithm. In the learning, information described in the CIF of various materials is used as input data, and a pseudo characteristic value approximately calculated from the information described in the CIF is used as correct answer data, and a calculation parameter may be determined using an error backpropagation method so as to output correct answer data for the input data. In addition, when a regression analyzer using CGCNN is adopted, 128 component values ​​directly used in the calculation of the pseudo characteristic value may be used as the intermediate vector. That is, the intermediate vector is a 128-dimensional vector. Then, the first principal component to the twelfth principal component obtained by the principal component analysis of the 128-dimensional intermediate vector may be adopted as components of the feature vector. In other words, the feature vector becomes a 12-dimensional vector.

[0038] In the prepared search space, as shown in FIG. 4B, the material points M corresponding to the candidate materials are arranged in the space spanned by the components of the feature vector (which is a one-dimensional space in the figure, but is actually a multidimensional space). 1 , M 2 , ... are distributed, and for materials whose target property value yi is known, the known target property value yi is associated with the material point. As will be described later, when a new target property value yi is detected in the detection process, the value is newly associated with the material point of the corresponding material (new addition). When the search space is prepared as described above, in the following process, a material whose target property value is closest to the target value yt in the search space is searched for.

[0039] (3) Gaussian process regression processing As already mentioned, in the search for materials in the search space, a material whose target characteristic value is predicted to be as close as possible to its target value is selected from among candidate materials whose target characteristic value is unknown (hereinafter referred to as "unknown material"). For this purpose, a probability distribution of predicted values ​​for the target characteristic value at the material point of the unknown material is obtained using the feature vector and the target characteristic value of the known material according to the Gaussian process regression model, and an expected value of the predicted value is obtained (step 8). In this embodiment, as an algorithm for obtaining such a probability distribution, any algorithm of a Gaussian process regression model may be adopted, and preferably, the Gaussian process regression model (ALEBO-GP) used in the ALEBO algorithm described in Non-Patent Document 3 may be used. In such ALEBO-GP, to put it simply, a kernel called a Mahalanobis kernel is adopted as the kernel which is the covariance matrix of the probability distribution of the predicted value, and the calculation range is set smaller than usual, so that it is possible to efficiently perform calculations and reduce the calculation load even when the feature vector is high-dimensional. In the embodiment, the algorithm described in Non-Patent Document 3 may be used as is. In addition, in calculating the probability distribution of the predicted value, it is necessary to calculate the inverse matrix of the kernel, and for such calculation, the CIQ algorithm described in Non-Patent Document 4 is advantageously used.

[0040] As already mentioned, it has been found that the inverse of the Poisson loss Lp (Equation (1)), normalized Poisson loss Lp' (Equation (1a)), or square error Le (Equation (1b)) between the target property value and the target value is advantageously used as the predicted value for which the probability distribution is calculated for each candidate material, that is, the evaluation function optimized when the target property value approaches the target value. Therefore, in one aspect of this embodiment, in step 8, the probability distribution of the predicted value of the inverse of the Poisson loss Lp (or normalized Poisson loss Lp' or square error Le) between the target property value and the target value at each material point may be preferably calculated. For this purpose, in step 8, first, the target value of the target property value is set, and then the probability distribution of the predicted value at each material point is calculated. FIG. 5(A) is a diagram showing a schematic representation of the probability distribution of predicted values ​​at material points. As can be seen from the diagram, in step 8, for each material point, a probability distribution P of the predicted value of the inverse of the Poisson loss Lp (or the normalized Poisson loss Lp' or the square error Le) between the target characteristic value and the target value is calculated. M1 , P M2 , ... are determined. Then, at each material point, the expected value of 1 / Lp (or 1 / Lp' or 1 / Le) is calculated from each probability distribution.

[0041] (4) Thompson extraction process Thus, in this embodiment, once the expected value of the predicted value for the target property value of each material point is obtained by the above Gaussian process regression process, a material whose target property value is predicted to be as close as possible to its target value is selected according to the Thompson extraction algorithm (step 9). In Thompson extraction, a probability is calculated for each material point such that the larger the expected value of the predicted value for the target property value, the higher the probability that the material point will be selected. Specifically, for each material point M i The probability of selection of Ps(M i ) may be a softmax function of such expectations, Ps(M i )=e μi / Σe μi …(2) where μi is the material point M iΣ is the expected value of the predicted value for each material point, and Σ is the sum for all material points. Here, when the predicted value is the inverse of the Poisson loss Lp (or the normalized Poisson loss Lp' or the square error Le) between the target property value and the target value as described above, the smaller the difference between the target property value and the target value, the larger the predicted value becomes, and therefore the higher the selection probability given by the above formula (2). FIG. 5(B) shows the selection probability for each material point M i As can be seen from the figure, the selection probability for each material point M i The selection probability at each material point M i The value is set according to the expected value of the predicted value.

[0042] Thereafter, the material whose target characteristic value is predicted to be as close as possible to the target value, i.e., the material whose target characteristic value is to be accurately detected next, is selected for each material point M i In this method of selecting or extracting materials, the material points are not selected assuming that the material points are continuously distributed in the search space, but rather, a machine exists that gives rewards with the probability of each expected value depending on the number of material points, and the material point is selected so that the largest reward can be obtained from among them. In fact, in the search space, the material points are not continuously present, but are discretely scattered, so bandit optimization is considered to be more suitable for searching for material points.

[0043] (5) Detection of target characteristic values ​​of materials As described above, when one material is selected from the candidate materials as a material whose target property value is predicted to be as close as possible to its target value, the target property value of that material is detected by any method (step 10). Here, in order to determine whether the selected material truly has the target property, the target property value is detected as accurately as possible. Specifically, the target property value is detected by actual measurement or by highly accurate calculation or simulation. Then, if the detected target property value is sufficiently close to the target value and it is determined that the selected material truly has the target property, for example, for a small number ε that is set arbitrarily, |target value-detected value|<ε …(3) When the above holds (step 11), the search for materials ends (step 12). On the other hand, when searching for a material whose target property value is closer to the target value than the detected target property value, the above process from step 6 is repeated. At that time, the material whose target property value has been newly detected is added as a known material, and the newly detected target property value is associated with that material point, and the subsequent processes are executed. With this configuration, as already mentioned, the more the processing cycle is repeated, the more the number of known materials increases, and this improves the accuracy of the regression process, so that it is expected that a material whose target property value is predicted to be as close as possible to its target value can be selected more accurately.

[0044] In this embodiment, the above process cycle may be terminated after being repeated an arbitrarily set number of times. In this case, the number C of process cycles is counted (step 7), and when the number C of cycles reaches a predetermined value Ct that is arbitrarily set (step 11), the search for materials may be terminated (step 12).

[0045] Experimental Example According to the teaching of the present embodiment, the laboratory's CIF and information on the target characteristic value were used, the band gap of the material was used as the target characteristic value, the target value was set to 2.534 eV, and a simulation experiment was carried out to search for a material whose band gap is as close as possible to the target value, thereby verifying the effectiveness of the present embodiment. It should be understood that the following experimental example is intended to illustrate the effectiveness of the present embodiment, and does not limit the scope of the present invention.

[0046] In the experiment, a regression analyzer according to CGCNN described in Non-Patent Document 2 was used to prepare the search space. Specifically, first, the band gap was calculated as a pseudo characteristic value by DFT calculation using VASP (Vienna Ab initio Simulation Package) from the information of 35180 CIFs of 6218 types of materials owned by the laboratory, and the information of the 35180 CIFs and each pseudo characteristic value were used as learning data to train the regression analyzer according to the learning algorithm of CGCNN. Then, of the 35180 CIFs, one CIF was selected for each of the 6218 types of materials and input into the trained regression analyzer, and the 6218 types of materials were used as candidate materials to calculate a 128-dimensional intermediate vector for each material. Furthermore, principal component analysis was applied to these intermediate vectors, and the first principal component to the 12th principal component were adopted as components of the feature vector. In addition, although the band gap values ​​of all 6218 types of materials are known to a high degree of accuracy, the band gaps of 100 types were set as known and the remaining 6118 types were set as unknown, and the problem was set so that the band gaps of unknown materials would become known when the materials were selectively extracted and the band gaps of the materials were selectively detected. In the regression and extraction processes, ALEBO-GP was adopted as a Gaussian process regression model, and the inverse of the Poisson loss Lp in formula (1) was used as the predicted value (evaluation function) for the target characteristic value to be optimized (however, when the target value was set to 2.534 eV and the target characteristic value ≦ 0, the inverse of Le in formula (1b) was used as the evaluation function), and the CIQ algorithm was used to calculate the probability distribution.

[0047] 6, when comparing the change in the absolute value of the error (MAE) between the characteristic value and the target value of the optimum material versus the number of searches (number of trials) when the above-mentioned material search was performed by the method of this embodiment, the Bayesian optimization method, and the random extraction method, the MAE at the time when the number of searches was 3 in the case of the method of this embodiment was approximately the same as the MAE at the time when the number of searches was 30 in the conventional method using Bayesian optimization. In other words, according to this result, it can be said that the method of this embodiment has a search efficiency about 10 times higher than that of the method using Bayesian optimization.

[0048] The table also shows the contribution of each process to the results in this embodiment. [Table 1] In the above, each notation is as follows. GCN+PCA: Calculate feature vectors using CGCNN and principal component analysis GCN: Uses intermediate vectors of CGCNN as feature vectors Crystal information: Information in CIF is used for feature vector Crystal information + PCA: Principal components obtained by applying principal component analysis to the information in the CIF are used as feature vectors ALEBO-GP: ALEBO-GP is used for the Gaussian process regression model. Normal-GP: Adopting a normal model for Gaussian process regression model Thompson: Thompson extraction is used to selectively extract materials. UCB: A Bayesian optimization method using upper confidence bound as the acquisition function is used for material selection and extraction. Poisson: The inverse of the Poisson loss Lp between the target characteristic value and the target value is used as the optimized value (evaluation function). (However, when the target characteristic value is ≦ 0, the inverse of Le is used.) Absolute error value: The absolute value of the difference between the target characteristic value and the target value is used as the optimized value (evaluation function). MAE: The average MAE for the 30th trial in a 50-cycle search experiment

[0049] As can be seen from the first and second rows of the results in Table 1 above, when Thompson extraction is used for selective extraction of materials as in this embodiment, it is understood that the MAE is reduced significantly. Also, according to the teachings of this embodiment, it is understood that the MAE is reduced when CGCNN and principal component analysis are used for calculating the feature vector, ALEBO-GP is used as the Gaussian process regression model, or the reciprocal of the absolute value of the Poisson loss between the target characteristic value and the target value is used as the value to be optimized.

[0050] Thus, as described above, it has been suggested that the method of the present embodiment can reduce the number of searches required to find a material having properties that match the desired properties as closely as possible or sufficiently. The method of the present embodiment may be similarly applied to any physical quantity other than the band gap as the target property value.

[0051] The above description has been given in relation to the embodiment of the present invention, but it will be apparent to those skilled in the art that many modifications and changes can be easily made thereto, and that the present invention is not limited to the embodiment exemplified above, but can be applied to various devices without departing from the concept of the present invention.

Claims

1. A method for searching for materials having target properties by a computer device, comprising: A first step of preparing a feature vector having a correlation with a target characteristic value for each of a plurality of candidate materials; a second step of calculating a probability distribution of the target characteristic value from the feature vector for each of the candidate materials in accordance with a Gaussian process regression model algorithm using a target characteristic value of a known material among the candidate materials, the target characteristic value of which is known, and the feature vector; a third step of selecting, from among the candidate materials, a material whose target property value is predicted to be closest to its target value according to a Thompson selection algorithm based on a probability distribution for the target property value of each of the candidate materials; a fourth step of determining the target property value of the selected material; Including, A method of repeating the second, third and fourth steps until a predetermined condition is met, by including the selected material, whose target characteristic value has been determined in the fourth step, in known materials whose target characteristic value is known.

2. 2. The method according to claim 1, wherein in the first step, the feature vector is calculated based on crystal information of each of a plurality of candidate materials.

3. 3. The method according to claim 2, wherein in the first step, the feature vector is calculated using a regression analyzer that calculates target characteristic values ​​from crystal information of an arbitrary material.

4. 4. The method of claim 3, wherein in the first step, the regression analyzer is a regression analyzer configured according to a crystal graph convolution neural network algorithm trained to calculate a target characteristic value determined by first-principles calculation from crystal information of a plurality of materials.

5. 5. The method of claim 4, wherein in the first step, an intermediate vector used in calculating the target characteristic value in the regression analyzer for each of the plurality of candidate materials is extracted, and a predetermined number of principal components obtained by principal component analysis of the intermediate vectors of the plurality of candidate materials, the number of principal components being less than the number of dimensions of the intermediate vector, are used as the feature vector.

6. 6. A method according to claim 1, wherein in the second step, the probability distribution for the target characteristic value is a probability distribution of the inverse of Poisson loss, normalized Poisson loss or squared error between the target characteristic value and the target value, and in the third step, a Thompson extraction algorithm is used to select from the candidate materials a material whose target characteristic value is predicted to be closest to the target value according to a probability calculated so that the larger the expected value of the Poisson loss, normalized Poisson loss or squared error, the larger the probability becomes.

7. 7. The method according to claim 1, wherein in the second step, the Gaussian process regression model algorithm follows ALEBO's algorithm and a Mahalanobis kernel is used as a kernel that gives the probability distribution.

8. 8. The method according to claim 7, wherein in the calculation of the probability distribution using the Mahalanobis kernel, a CIQ algorithm is used for computing an inverse matrix of the Mahalanobis kernel.

9. A system for assisting in the search for materials having desired properties, comprising: A first means for preparing a feature vector having a correlation with a target characteristic value for each of a plurality of candidate materials; a second means for calculating a probability distribution of the target characteristic value from the feature vector for each of the candidate materials in accordance with an algorithm of a Gaussian process regression model using a target characteristic value of a known material, the target characteristic value of which is known, and the feature vector; a third means for selecting, from among the candidate materials, a material whose target property value is predicted to be closest to its target value according to a Thompson selection algorithm based on a probability distribution for the target property value of each of the candidate materials; A system including:

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